Module dae 

Differential Algebraic Equation (DAE) solvers

This module provides numerical solvers for differential algebraic equations (DAEs). DAEs are a more general class of equations than ODEs and include algebraic constraints.

Features:

• Support for index-1 DAE systems
• Semi-explicit DAE solvers for specialized forms
• Implicit DAE solvers for general forms
• Integration with mass matrix functionality
• Specialized BDF methods for DAE systems

DAEs can be classified based on their index, which roughly corresponds to the number of times one must differentiate the constraint equations to obtain an ODE. This module focuses primarily on index-1 DAEs, which are the most common in practice.

Semi-explicit Form

Semi-explicit DAEs have the form:

x' = f(x, y, t)
0 = g(x, y, t)

where x are differential variables and y are algebraic variables.

Fully-implicit Form

Fully-implicit DAEs have the form:

F(t, y, y') = 0

where all variables are treated uniformly and the system equations depend on both the variables and their derivatives.

Re-exports

pub use self::types::DAEIndex;

pub use self::types::DAEOptions;

pub use self::types::DAEResult;

pub use self::types::DAEType;

pub use self::solvers::solve_higher_index_dae;

pub use self::solvers::solve_implicit_dae;

pub use self::solvers::solve_ivp_dae;

pub use self::solvers::solve_semi_explicit_dae;

pub use self::methods::bdf_dae::bdf_implicit_dae;

pub use self::methods::bdf_dae::bdf_semi_explicit_dae;

pub use self::methods::index_reduction_bdf::bdf_implicit_with_index_reduction;

pub use self::methods::index_reduction_bdf::bdf_with_index_reduction;

pub use self::methods::krylov_dae::krylov_bdf_implicit_dae;

pub use self::methods::krylov_dae::krylov_bdf_semi_explicit_dae;

pub use self::methods::block_precond::create_block_ilu_preconditioner;

pub use self::methods::block_precond::create_block_jacobi_preconditioner;

pub use self::index_reduction::DAEStructure;

pub use self::index_reduction::DummyDerivativeReducer;

pub use self::index_reduction::PantelidesReducer;

pub use self::index_reduction::ProjectionMethod;

Modules

index_reduction

Index reduction techniques for higher-index DAE systems

methods

Methods for solving Differential Algebraic Equations (DAEs)

solvers

DAE solver implementations

types

Types for DAE solver module

utils

Utility functions for DAE solvers